The distribution of wages and jobs changed all across advanced economies the last few decades. These changes came seemingly unexpected. Economic theory tell us to look at supply and demand to understand what happened. In practice, we cannot directly observe demand and supply shifts. We also cannot easily distinguish the economic forces behind these distributional changes from other concurrent phenomena. These fundamental problems permeate all studies of changes in the wage and occupational distributions. This dissertation applies two approaches to overcome these challenges. In the first chapter (with Tzuo-Hann Law), we take an assortative matching model with on-the-job search and use it understand what forces drove up wage inequality in Ger...